Finite Group Databasebeta

C2×C22⋊#15692550 #39910214

order26176
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#15692550

Splittings

SylowC409 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC23C2×#13109888
commutatorC2×C409C22×C8
FrattiniC22C22×#13109888
Fitting, prime radicalC24×C409C4
socleC23×C409C2×C4
cosocleC2×Dic409C23
hypercenterC24#13109888
hypocenterC409C2×C22⋊C8
LCSG ▷ C2×C409 ▷ C409
UCSC1 ◁ C23 ◁ C24

202 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, 1516);