Finite Group Databasebeta

C2×C4×C4⋊C4×D13 #16021095

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C4×C4⋊C4×D13

Splittings

FittingC2×C4×C13×C4⋊C4 ⋊ C2
SylowC13 ⋊ C22×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC2×C13C23×C42
FrattiniC23C24×D13
FittingC2×C4×C13×C4⋊C4C2
socleC24×C13C24
prime radicalC24×D13C23
cosocleC23×C13C25
hypercenterC2×C4×C4⋊C4D13
hypocenterC13C22×C4×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 327744);