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C₂×#16837158 #21423796

order	7552
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³×C₄

Aliases

C₂×#16837158

Splittings

C₅₉ ⋊ C₂×H(3,ℤ/4)

Subgroups

	subgroup	G/H
center	C₂×C₄	C₄×Dic₅₉
commutator	C₄×C₅₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₂×#117×C₅₉	C₂
socle	C₂²×C₅₉	#95
hypercenter	C₂×#117	D₅₉
hypocenter	C₅₉	C₂×H(3,ℤ/4)
LCS	G ▷ C₄×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117

404 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1204 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	H(3,ℤ/4)×Dic₅₉, C₄×#16837158, #28493857, …
maximal normal subgroup of	H(3,ℤ/4)×Dic₅₉, C₄×#16837158, #28493857, …
maximal quotient of	C₂×#21421924, C₂×#21421925, #28478087, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7552, 4210);