Finite Group Databasebeta

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C₈×D₇₇₂ #27135326

order	12352
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₈×D₇₇₂

Splittings

Fitting	C₄×C₈×C₁₉₃ ⋊ C₂
Sylow	C₁₉₃ ⋊ C₈×D₄

Subgroups

	subgroup	G/H
center	C₂×C₈	C₂×D₁₉₃
commutator	C₂×C₁₉₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₁₉₃
Fitting	C₄×C₈×C₁₉₃	C₂
socle	C₂²×C₁₉₃	C₂²×C₄
prime radical	C₂×D₇₇₂	C₄
cosocle	C₂×C₄×C₁₉₃	C₂³
hypercenter	C₄×C₈	D₁₉₃
hypocenter	C₁₉₃	C₈×D₄
LCS	G ▷ C₂×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 616);