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C3×C72×D85 #38735986

order24990
automorphism?
homologyAbelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7

Aliases

direct productC3×C72×D85
unambiguous semidirect productC5⋊(C3×C72×D17)
unambiguous semidirect productC17⋊(C3×C72×D5)

Splittings

Fitting, socle, HallC3×C5×C72×C17 ⋊ C2
derived, HallC5×C17 ⋊ C2×C3×C72
HallC5×C72×C17 ⋊ C2×C3
HallC3×C72×C17 ⋊ D5
HallC72×C17 ⋊ C3×D5
HallC3×C5×C72 ⋊ D17
HallC3×C5×C17 ⋊ C2×C72
HallC5×C72 ⋊ C3×D17
HallC3×C17 ⋊ C72×D5
SylowC17 ⋊ C3×C72×D5
HallC3×C5 ⋊ C72×D17
SylowC5 ⋊ C3×C72×D17

Subgroups

subgroupG/H
center, hypercenterC3×C72D85
commutator, cosocle, hypocenterC5×C17C2×C3×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C17C2
LCSG ▷ C5×C17
UCSC1 ◁ C3×C72

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12495

Conjugacy classes & character table

6468 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 76);