Finite Group Databasebeta

C2×#27189792 #39910304

order26176
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27189792

Splittings

SylowC409 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C4C2×#13109888
commutatorC2×C409C22×C8
FrattiniC4C22×#13109888
FittingC2×C8×C409C4
socleC22×C409C2×C8
prime radicalC22×D409C8
cosocle#15692543C23
hypercenterC2×C8#13109888
hypocenterC409C2×M32
LCSG ▷ C2×C409 ▷ C409
UCSC1 ◁ C2×C4 ◁ C2×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13088

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, 1606);