Finite Group Databasebeta

C23×#88100 #16807996

order3328
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210

Aliases

direct productC23×#88100

Splittings

FittingC23×C8×C13 ⋊ C4
SylowC13 ⋊ C23×#97

Subgroups

subgroupG/H
centerC23×C4C2×#261
commutatorC2×C13C23×C42
FrattiniC4C24×#261
FittingC23×C8×C13C4
socleC24×C13C42
prime radicalC24×D13C2×C4
cosocleC4×D13C25
hypercenterC23×C8#261
hypocenterC13C23×#97
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C23×C8

4126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114645);