Finite Group Databasebeta

C2×#20295899 #28378715

order13952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20295899

Splittings

FittingC2×C4⋊C4×C109 ⋊ C4
SylowC109 ⋊ C2×#340

Subgroups

subgroupG/H
centerC23C22⋊#89137
commutatorC4×C109C2×C42
FrattiniC2×C4C22×#89137
FittingC2×C4⋊C4×C109C4
socleC23×C109C22⋊C4
prime radicalC23×D109D4
cosocleC2×C4×D109C23
hypercenterC2×C4⋊C4#89137
hypocenterC109C2×#340
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20193);