Finite Group Databasebeta

C4×C4⋊C4×D31 #16848044

order3968
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×C4⋊C4×D31

Splittings

FittingC4×C4⋊C4×C31 ⋊ C2
SylowC31 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C22×D31
commutatorC2×C31C22×C42
FrattiniC23C23×D31
FittingC4×C4⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC23×D31C23
hypercenterC4×C4⋊C4D31
hypocenterC31C2×C4×C4⋊C4
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 6843);