Finite Group Databasebeta

C22×#20266996 #39910318

order26176
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#20266996

Splittings

derived, SylowC409 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#13109888
commutator, hypocenterC409C23×C8
FrattiniC2C23×#13109888
FittingC22×C4×C409C4
socleC23×C409C2×C4
prime radicalC23×D409C4
cosocleDic409C24
LCSG ▷ C409
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13088

Conjugacy classes & character table

1696 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 1620);