Finite Group Databasebeta

C2×#27189674 #39909701

order26176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#27189674

Splittings

FittingC2×C42×C409 ⋊ C2
SylowC409 ⋊ C2×#117

Subgroups

subgroupG/H
centerC22×C4C2×D409
commutatorC2×C409C23×C4
FrattiniC22C23×D409
FittingC2×C42×C409C2
socleC23×C409C23
prime radicalC23×D409C22
cosocleC22×C409C24
hypercenterC2×C42D409
hypocenterC409C2×#117
LCSG ▷ C2×C409 ▷ C409
UCSC1 ◁ C22×C4 ◁ C2×C42

330 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, 1003);