Finite Group Databasebeta

C22×#19154561 #37554946

order23488
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#19154561

Splittings

SylowC367 ⋊ C22×M16

Subgroups

subgroupG/H
centerC22×C4C2×D367
commutatorC2×C367C23×C4
FrattiniC4C23×D367
FittingC23×C4×C367C2
socleC23×C367C2×C4
prime radicalC24×C367C4
cosocleC4×C367C24
hypercenterC23×C4D367
hypocenterC367C22×M16
LCSG ▷ C2×C367 ▷ C367
UCSC1 ◁ C22×C4 ◁ C23×C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

5896 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 1309);