Finite Group Databasebeta

C2×C22⋊#15692543 #39909208

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

Aliases

direct productC2×C22⋊#15692543

Splittings

SylowC409 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D409
commutatorC2×C409C22×C8
FrattiniC2×C4C22×D409
FittingC23×C4×C409C2
socleC23×C409C2×C4
prime radicalC24×C409C4
cosocleC2×C4×C409C23
hypercenterC23×C4D409
hypocenterC409C2×C22⋊C8
LCSG ▷ C2×C409 ▷ C409
UCSC1 ◁ C22×C4 ◁ C23×C4

202 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, 510);