Finite Group Databasebeta

C2×#20295078 #28371647

order13952
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20295078

Splittings

FittingC2×C4⋊C8×C109 ⋊ C2
SylowC109 ⋊ C2×#431

Subgroups

subgroupG/H
centerC22×C4C22×D109
commutatorC2×C109C23×C8
FrattiniC2×C4C23×D109
FittingC2×C4⋊C8×C109C2
socleC23×C109C22×C4
prime radicalC23×D109C2×C4
cosocleC2×C4×C109C24
hypercenterC2×C4⋊C8D109
hypocenterC109C2×#431
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13125);