C₂×#26018180 #36463507

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×#26018180

Splittings

Sylow

C₈₉ ⋊ C₂×#1316

Subgroups

	subgroup	G/H
center	C₂³	#15667927
commutator	C₂³×C₈₉	C₂²×C₈
Frattini	C₂×C₂²⋊C₄	C₂²×D₈₉
Fitting	C₂×#379×C₈₉	C₂
socle	C₂³×C₈₉	#99
prime radical	C₂⁶×C₈₉	C₄
cosocle	C₂×C₂²⋊C₄×C₈₉	C₂³
hypercenter	C₂×#379	D₈₉
hypocenter	C₈₉	C₂×#1316
LCS	G ▷ C₂³×C₈₉ ▷ C₂²×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴ ◁ C₂²×C₂²⋊C₄ ◁ C₂×#379

1886 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1886 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 107
transitive degree	μ_t(G) = 2848

A minimal faithful permutation representation — 3 generators on 107 points:

(12,15)(16,17)(19,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21);(3,4,5,7,6,8,9,10)(11,12)(13,17,18,15)(14,16)(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);(1,2)

Conjugacy classes & character table

2516 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 78647);