C₈×C₇₉⋊C₃₂ #34175595

order	20224
automorphism	?
homology	Abelianization (H₁) = C₈×C₃₂ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₈×C₇₉⋊C₃₂

Splittings

derived, Sylow

C₇₉ ⋊ C₈×C₃₂

Subgroups

	subgroup	G/H
center, hypercenter	C₈×C₁₆	D₇₉
commutator, hypocenter	C₇₉	C₈×C₃₂
Frattini	C₄×C₁₆	C₂×D₇₉
Fitting	C₈×C₁₆×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₄×C₁₆
cosocle	C₄×C₁₆×C₇₉	C₂²
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₈×C₁₆

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 20224

A minimal faithful permutation representation — 2 generators on 119 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)(88,89,90,94,91,95,98,104,92,96,99,105,101,107,110,114,93,97,100,106,102,108,111,115,103,109,112,116,113,117,118,119);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,81,82,84,83,85,86,87)

Conjugacy classes & character table

5248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 56894);

C8×C79⋊C32 #34175595