C₈₉×D₉₇ #31772147

order	17266
isoclinism	isoclinic class of D₉₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₈₉×D₉₇
unambiguous semidirect product	C₉₇⋊(C₂×C₈₉)

Splittings

Fitting, socle, Hall	C₈₉×C₉₇ ⋊ C₂
derived, Sylow	C₉₇ ⋊ C₂×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₈₉	D₉₇
commutator, cosocle, hypocenter	C₉₇	C₂×C₈₉
Frattini	C₁	G
Fitting, socle	C₈₉×C₉₇	C₂
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₈₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 186
transitive degree	μ_t(G) = 8633

A minimal faithful permutation representation — 2 generators on 186 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)

Conjugacy classes & character table

4450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₈₉×#87604, #46828720, D₈₉×D₉₇, …
maximal normal subgroup of	C₈₉×#87604, #46828720, D₈₉×D₉₇, …
maximal quotient of	C₈₉×Dic₉₇, C₂×C₈₉×D₉₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17266, 2);

C89×D97 #31772147