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C22×D17⋊#101 #17979484

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×D17⋊#101
unambiguous semidirect productD17⋊(C22×#101)

Splittings

SylowC17 ⋊ C23×#101

Subgroups

subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC23×Q8×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17C2×C4
cosocleC2×Dic17C25
hypercenterC23×Q8#595
hypocenterC17C23×#101
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

4990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114728);