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C5×C17×C3⋊(C7⋊D7) #38735995

order24990
automorphism?
homologyAbelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C7

Aliases

direct productC5×C17×C3⋊(C7⋊D7)
unambiguous semidirect productC3⋊(C5×C17×C7⋊D7)
unambiguous semidirect productC7⋊(C5×C17×D21)

Splittings

Fitting, socle, HallC3×C5×C72×C17 ⋊ C2
derived, HallC3×C72 ⋊ C2×C5×C17
HallC5×C72×C17 ⋊ D3
HallC3×C72×C17 ⋊ C2×C5
HallC72×C17 ⋊ C5×D3
HallC3×C5×C72 ⋊ C2×C17
HallC3×C5×C17 ⋊ C7⋊D7
HallC5×C72 ⋊ D3×C17
HallC3×C17 ⋊ C5×C7⋊D7
SylowC72 ⋊ C5×D3×C17
HallC3×C5 ⋊ C17×C7⋊D7
SylowC3 ⋊ C5×C17×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC5×C17C3⋊(C7⋊D7)
commutator, cosocle, hypocenterC3×C72C2×C5×C17
FrattiniC1G
Fitting, socleC3×C5×C72×C17C2
LCSG ▷ C3×C72
UCSC1 ◁ C5×C17

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12495

Conjugacy classes & character table

6375 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 85);