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C2×#135×#595 #17979754

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#135×#595
unambiguous semidirect productD17⋊(C4×#135)

Splittings

FittingC2×C17×#135 ⋊ C4
SylowC17 ⋊ C2×C4×#135

Subgroups

subgroupG/H
centerC2×C4D4×#595
commutatorC4×C17C24×C4
FrattiniC4C24×#595
FittingC2×C17×#135C4
socleC22×C17C2×C4×D4
prime radicalC2×#135×D17C2
cosocleC4×D17C25
hypercenterC2×#135#595
hypocenterC17C2×C4×#135
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114998);