Finite Group Databasebeta

C2×#27189772 #39910205

order26176
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27189772

Splittings

SylowC409 ⋊ C2×#97

Subgroups

subgroupG/H
centerC23C2×#13109888
commutatorC2×C409C2×C42
FrattiniC22C22×#13109888
FittingC22×C4×C409C4
socle, prime radicalC23×C409C2×C4
cosocleC2×Dic409C23
hypercenterC22×C4#13109888
hypocenterC409C2×#97
LCSG ▷ C2×C409 ▷ C409
UCSC1 ◁ C23 ◁ C22×C4

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26176

Conjugacy classes & character table

1672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 1507);