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C72×D255 #38735998

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

Aliases

direct productC72×D255
unambiguous semidirect productC3⋊(C72×D85)
unambiguous semidirect productC5⋊(C72×D51)
unambiguous semidirect productC17⋊(C72×D15)

Splittings

Fitting, socle, HallC3×C5×C72×C17 ⋊ C2
derived, HallC3×C5×C17 ⋊ C2×C72
HallC5×C72×C17 ⋊ D3
HallC3×C72×C17 ⋊ D5
HallC72×C17 ⋊ D15
HallC3×C5×C72 ⋊ D17
HallC5×C72 ⋊ D51
HallC3×C72 ⋊ D85
HallC5×C17 ⋊ D3×C72
HallC3×C17 ⋊ C72×D5
SylowC17 ⋊ C72×D15
HallC3×C5 ⋊ C72×D17
SylowC5 ⋊ C72×D51
SylowC3 ⋊ C72×D85

Subgroups

subgroupG/H
center, hypercenterC72D255
commutator, cosocle, hypocenterC3×C5×C17C2×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C17C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C72

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12495

Conjugacy classes & character table

6321 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 88);