Finite Group Databasebeta

C4×C4⋊#11745400 #28417374

order14912
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C4⋊#11745400

Splittings

FittingC42×C233 ⋊ C4
SylowC233 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC2×C4C2×#11745400
commutatorC2×C233C2×C42
FrattiniC22C22×#11745400
FittingC42×C233C4
socleC22×C233C22×C4
prime radical, cosocleC22×D233C23
hypercenterC42#11745400
hypocenterC233C4×C4⋊C4
LCSG ▷ C2×C233 ▷ C233
UCSC1 ◁ C2×C4 ◁ C42

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3728

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 1488);