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C₁₃×C₁₇⋊D₁₇ #21418928

order	7514
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₁₇

Aliases

direct product	C₁₃×C₁₇⋊D₁₇
unambiguous semidirect product	C₁₇⋊(C₁₃×D₁₇)

Splittings

Fitting, socle, Hall	C₁₃×C₁₇² ⋊ C₂
derived, Sylow	C₁₇² ⋊ C₂×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	C₁₇⋊D₁₇
commutator, hypocenter	C₁₇²	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₇²	C₂
LCS	G ▷ C₁₇²
UCS	C₁ ◁ C₁₃

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1898 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₃×#11923883, C₁₃×#11923884, C₁₃×D₁₇², …
maximal normal subgroup of	C₁₃×#11923883, C₁₃×#11923884, C₁₃×D₁₇², …
maximal quotient of	C₁₃×#11923880, C₂×C₁₃×C₁₇⋊D₁₇, C₃×C₁₃×C₁₇⋊D₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7514, 7);