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#23780607

order	10374
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₇×C₁₃×C₁₉ ⋊ C₂×C₃
Hall	C₇×#10625203 ⋊ C₂
Hall	C₁₉×D₉₁ ⋊ C₃
Hall	#10625203 ⋊ D₇
Hall	C₁₃×C₁₉ ⋊ C₃×D₇
Hall	D₉₁ ⋊ C₁₉⋊C₃
Hall	C₇×C₁₉ ⋊ D₁₃⋊C₃
Hall	C₇×C₁₃ ⋊ C₂×C₁₉⋊C₃
Sylow	C₁₉ ⋊ (C₁₃⋊C₃)⋊D₇
Sylow	C₁₃ ⋊ D₇×C₁₉⋊C₃
Sylow	C₇ ⋊ #13093365

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₁₉
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,7,13,19|c^a=c^6,d^a=d^12,d^b=d^3,e^b=e^11

Conjugacy classes & character table

311 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#13093361⋊D₇, #13093367⋊D₇, D₇×#13093365, …
maximal normal subgroup of	#13093361⋊D₇, #13093367⋊D₇, D₇×#13093365, …
maximal quotient of	#35208870, C₂×#23780607, #44527615, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 98);