Finite Group Databasebeta

C2×#27189724 #39910010

order26176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27189724

Splittings

SylowC409 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D409
commutatorC2×C409C23×C4
FrattiniC4C23×D409
Fitting, prime radicalC2×#41×C409C2
socleC22×C409C22×C4
cosocleC4×C409C24
hypercenterC2×#41D409
hypocenterC409C2×#131
LCSG ▷ C2×C409 ▷ C409
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13088

Conjugacy classes & character table

4120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 1312);