Finite Group Databasebeta

C22×#20266965 #39909694

order26176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#20266965

Splittings

FittingC23×C4×C409 ⋊ C2
SylowC409 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D409
commutatorC2×C409C23×C4
FrattiniC22C23×D409
FittingC23×C4×C409C2
socleC24×C409C22
prime radicalC24×D409C2
cosocleC22×C409C24
hypercenterC23×C4D409
hypocenterC409C22×C22⋊C4
LCSG ▷ C2×C409 ▷ C409
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13088

Conjugacy classes & character table

6568 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 996);