Finite Group Databasebeta

C23×(C2×#261)⋊C4 #16807441

order3328
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C212

Aliases

direct productC23×(C2×#261)⋊C4
unambiguous semidirect productD13⋊(C22×#95)

Splittings

FittingC24×C4×C13 ⋊ C4
SylowC13 ⋊ C23×#95

Subgroups

subgroupG/H
centerC25C2×#261
commutatorC2×C13C23×C42
FrattiniC22C24×#261
FittingC24×C4×C13C4
socleC25×C13C2×C4
prime radicalC25×D13C22
cosocleC22×D13C25
hypercenterC24×C4#261
hypocenterC13C23×#95
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×C4

14334 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, 1114090);