Finite Group Databasebeta

C23×C22⋊D373 #37560243

order23872
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC23×C22⋊D373

Splittings

FittingC25×C373 ⋊ C2
SylowC373 ⋊ C23×D4

Subgroups

subgroupG/H
centerC24C2×D373
commutator, cosocleC2×C373C25
FrattiniC2C24×D373
FittingC25×C373C2
socleC24×C373C22
hypercenterC25D373
hypocenterC373C23×D4
LCSG ▷ C2×C373 ▷ C373
UCSC1 ◁ C24 ◁ C25

1362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11936

Conjugacy classes & character table

5992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23872, 1370);