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C₂²×D₁₄₉⋊C₈ #23750696

order	9536
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product	C₂²×D₁₄₉⋊C₈
unambiguous semidirect product	D₁₄₉⋊(C₂²×C₈)

Splittings

C₁₄₉ ⋊ C₂³×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₄	#10597010
commutator, hypocenter	C₁₄₉	C₂³×C₈
Frattini	C₂	C₂³×#10597010
Fitting	C₂²×C₄×C₁₄₉	C₄
socle	C₂³×C₁₄₉	C₂×C₄
prime radical	C₂³×D₁₄₉	C₄
cosocle	Dic₁₄₉	C₂⁴
LCS	G ▷ C₁₄₉
UCS	C₁ ◁ C₂²×C₄

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

656 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×(C₂×#10597010)⋊C₈, #34060352, #34060358, …
maximal normal subgroup of	C₂×(C₂×#10597010)⋊C₈, #34060352, #34060358, …
maximal quotient of	C₂²×C₄×#11924753, C₂×C₄×D₁₄₉⋊C₈, C₂×D₁₄₉⋊(C₂²⋊C₈), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 1620);