Finite Group Databasebeta

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C4⋊C4×D1033 #45683083

order33056
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×D1033

Splittings

FittingC4⋊C4×C1033 ⋊ C2
SylowC1033 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D1033
commutatorC2×C1033C22×C4
FittingC4⋊C4×C1033C2
socle, cosocleC22×C1033C23
prime radicalC22×D1033C22
hypercenterC4⋊C4D1033
hypocenterC1033C2×C4⋊C4
LCSG ▷ C2×C1033 ▷ C1033
UCSC1 ◁ C22 ◁ C4⋊C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16528

Conjugacy classes & character table

5180 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33056, 99);