Finite Group Databasebeta

C22×#16812774 #28379995

order13952
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16812774

Splittings

SylowC109 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C4C2×#89137
commutatorC2×C109C23×C8
FrattiniC4C23×#89137
FittingC22×C8×C109C4
socleC23×C109C2×C8
prime radicalC23×D109C8
cosocle#11724784C24
hypercenterC22×C8#89137
hypocenterC109C22×M32
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C22×C8

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

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, 21473);