Finite Group Databasebeta

C2×#27189708 #39909768

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

Aliases

direct productC2×#27189708

Splittings

SylowC409 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D409
commutator, cosocleC22×C409C24
FrattiniC22C23×D409
FittingC2×C4⋊C4×C409C2
socle, prime radicalC23×C409C23
hypercenterC2×C4⋊C4D409
hypocenterC409C2×#125
LCSG ▷ C22×C409 ▷ C409
UCSC1 ◁ C23 ◁ C2×C4⋊C4

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26176

Conjugacy classes & character table

4108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 1070);