Finite Group Databasebeta

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C4⋊C4×D991 #44540403

order31712
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×D991

Splittings

FittingC4⋊C4×C991 ⋊ C2
SylowC991 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D991
commutatorC2×C991C22×C4
FittingC4⋊C4×C991C2
socle, cosocleC22×C991C23
prime radicalC22×D991C22
hypercenterC4⋊C4D991
hypocenterC991C2×C4⋊C4
LCSG ▷ C2×C991 ▷ C991
UCSC1 ◁ C22 ◁ C4⋊C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15856

Conjugacy classes & character table

4970 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31712, 99);