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#117×Dic₇₉ #23765743

order	10112
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂³×C₄²

Aliases

#117×Dic₇₉

Splittings

C₇₉ ⋊ C₄×#117

Subgroups

	subgroup	G/H
center	C₂²×C₄	C₂²×D₇₉
commutator	C₂×C₇₉	C₂²×C₄²
Frattini	C₂³	C₂³×D₇₉
Fitting	C₂×#117×C₇₉	C₂
socle, cosocle	C₂³×C₇₉	C₂⁴
prime radical	C₂⁴×C₇₉	C₂³
hypercenter	C₂×#117	D₇₉
hypocenter	C₇₉	C₄×#117
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#117

752 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1640 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#34181710, #34181714, H(3,ℤ/4)×Dic₇₉, …
maximal normal subgroup of	#34181710, #34181714, H(3,ℤ/4)×Dic₇₉, …
maximal quotient of	#376×Dic₇₉, C₄×C₂²⋊C₄×Dic₇₉, C₄×C₄⋊C₄×Dic₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 6853);