Finite Group Databasebeta

C22×D13⋊#108 #16808154

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×D13⋊#108
unambiguous semidirect productD13⋊(C22×#108)

Splittings

SylowC13 ⋊ C23×#108

Subgroups

subgroupG/H
centerC22×C4C4⋊#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC23×C8×C13C4
socleC23×C13C2×C4⋊C4
prime radicalC24×D13Q8
cosocleC4×D13C25
hypercenterC23×C8#261
hypocenterC13C23×#108
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

2846 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114803);