Finite Group Databasebeta

← Prev (#10632543) Next (#10632545) →

C3×#13937 #10632544

order768
nilpotency class2
isoclinismisoclinic class of #2403
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productC3×#13937

Subgroups

subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC23×C3×#41C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

4470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 384

A minimal faithful permutation representation — 4 generators on 23 points:

(1,2,3)(5,7)(8,9,10,11)(13,15);(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(17,20)(21,23);(12,13)(14,15)(16,17)(18,21)(19,20)(22,23);(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,18,19,22)(17,21,20,23)

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of#72270863, #72270870, D3×#13937, …
maximal subgroup of#72270863, #72270870, C3×#647667, …
maximal normal subgroup of#72270863, #72270870, C3×#647667, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 6925);