Finite Group Databasebeta

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C4⋊C4×C4⋊Dic17 #16955763

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4⋊C4×C4⋊Dic17

Splittings

SylowC17 ⋊ C4⋊C42

Subgroups

subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC2×C4×C4⋊C4×C17C2
socle, prime radical, cosocleC24×C17C24
hypercenterC2×C4×C4⋊C4D17
hypocenterC17C4⋊C42
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

1838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 91007);