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C13×D357 #22604642

order9282
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D357
unambiguous semidirect productC3⋊(C13×D119)
unambiguous semidirect productC7⋊(C13×D51)
unambiguous semidirect productC17⋊(C13×D21)

Splittings

Fitting, socle, HallC3×C7×C13×C17 ⋊ C2
derived, HallC3×C7×C17 ⋊ C2×C13
HallC7×C13×C17 ⋊ D3
HallC3×C13×C17 ⋊ D7
HallC3×C7×C13 ⋊ D17
HallC13×C17 ⋊ D21
HallC7×C17 ⋊ D3×C13
HallC7×C13 ⋊ D51
HallC3×C17 ⋊ C13×D7
HallC3×C13 ⋊ D119
HallC3×C7 ⋊ C13×D17
SylowC17 ⋊ C13×D21
SylowC7 ⋊ C13×D51
SylowC3 ⋊ C13×D119

Subgroups

subgroupG/H
center, hypercenterC13D357
commutator, hypocenterC3×C7×C17C2×C13
FrattiniC1G
Fitting, socleC3×C7×C13×C17C2
LCSG ▷ C3×C7×C17
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2340 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×D17×D21, D13×D357, D221⋊D21, …
maximal normal subgroup ofC13×D17×D21, D13×D357, D221⋊D21, …
maximal quotient ofC13×Dic357, C2×C13×D357, C13×D1071, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 18);