Finite Group Databasebeta

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C2×C23×#449 #15670619

order2944
nilpotency class3
isoclinismisoclinic class of #447
automorphism?
homologyAbelianization (H1) = C24×C23 · Schur multiplier (H2) = C26

Aliases

direct productC2×C23×#449

Subgroups

subgroupG/H
center, socleC23×C23C2×D4
commutator, Frattini, cosocleC2×C4C24×C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C23×C4×C23 ◁ G

812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 1472

A minimal faithful permutation representation — 4 generators on 37 points:

(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(3,4)(5,6)(8,12)(9,10)(13,14);(7,8)(9,12)(10,14)(11,13);(4,6)(7,9,11,10)(8,12,13,14)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#9241, C4×C23×#449, C23×#21456, …
maximal normal subgroup ofC23×#9241, C4×C23×#449, C23×#21456, …
maximal quotient ofC2×C23×#1597, C2×C23×#1609, C2×C23×#1600, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1732);