Finite Group Databasebeta

C2×(C2×#89137)⋊C8 #28378691

order13952
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×(C2×#89137)⋊C8

Splittings

FittingC22×C8×C109 ⋊ C4
SylowC109 ⋊ C2×#336

Subgroups

subgroupG/H
centerC22×C4C2×#89137
commutatorC2×C109C2×C4×C8
FrattiniC2×C4C22×#89137
FittingC22×C8×C109C4
socleC23×C109C42
prime radicalC23×D109C2×C4
cosocleC2×C4×D109C23
hypercenterC22×C8#89137
hypocenterC109C2×#336
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C22×C8

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20169);