Finite Group Databasebeta

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C23×#88115 #16808092

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×#88115
unambiguous semidirect productD13⋊(C22×#102)

Splittings

FittingC23×D4×C13 ⋊ C4
SylowC13 ⋊ C23×#102

Subgroups

subgroupG/H
centerC24C22⋊#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC23×D4×C13C4
socleC24×C13C22⋊C4
prime radicalC23×D4×D13C2
cosocleC4×D13C25
hypercenterC23×D4#261
hypocenterC13C23×#102
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114741);