Finite Group Databasebeta

C2×#27189635 #39909226

order26176
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27189635

Splittings

SylowC409 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22#20266965
commutatorC22×C409C22×C4
FrattiniC2×C4C22×D409
FittingC2×M16×C409C2
socleC22×C409C22⋊C4
prime radicalC23×C409C2×C4
cosocleC2×C4×C409C23
hypercenterC2×M16D409
hypocenterC409C2×#101
LCSG ▷ C22×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13088

Conjugacy classes & character table

4102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 528);