Finite Group Databasebeta

C22×D373⋊C8 #37560493

order23872
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×D373⋊C8
unambiguous semidirect productD373⋊(C22×C8)

Splittings

derived, SylowC373 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#13093637
commutator, hypocenterC373C23×C8
FrattiniC2C23×#13093637
FittingC22×C4×C373C4
socleC23×C373C2×C4
prime radicalC23×D373C4
cosocleDic373C24
LCSG ▷ C373
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11936

Conjugacy classes & character table

1552 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23872, 1620);