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C5×C17⋊#64424 #38735947

order24990
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17⋊#64424
unambiguous semidirect productC17⋊(C5×#64424)

Splittings

Fitting, socle, HallC5×C72×C17 ⋊ C2×C3
derived, HallC72×C17 ⋊ C2×C3×C5
HallC5×C17×#3861 ⋊ C2
HallC5×C7⋊D119 ⋊ C3
HallC17×#3861 ⋊ C2×C5
HallC7⋊D119 ⋊ C3×C5
HallC5×#3861 ⋊ D17
HallC5×C72 ⋊ C3×D17
Hall#3861 ⋊ C5×D17
HallC5×C17 ⋊ #64424
SylowC72 ⋊ C3×C5×D17
SylowC17 ⋊ C5×#64424

Subgroups

subgroupG/H
center, hypercenterC5C17⋊#64424
commutator, cosocle, hypocenterC72×C17C2×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C17C2×C3
LCSG ▷ C72×C17
UCSC1 ◁ C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4165

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 37);