Finite Group Databasebeta

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C23×C4⋊C4×D17 #17940877

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productC23×C4⋊C4×D17

Splittings

FittingC23×C4⋊C4×C17 ⋊ C2
SylowC17 ⋊ C24×C4⋊C4

Subgroups

subgroupG/H
centerC25C22×D17
commutatorC2×C17C25×C4
FrattiniC22C25×D17
FittingC23×C4⋊C4×C17C2
socleC25×C17C23
prime radicalC25×D17C22
cosocleC22×C17C26
hypercenterC23×C4⋊C4D17
hypocenterC17C24×C4⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C25 ◁ C23×C4⋊C4

19742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076121);