Finite Group Databasebeta

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C11×Dic195 #22575045

order8580
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic195
unambiguous semidirect productC3⋊(C11×Dic65)

Splittings

derived, HallC3×C5×C13 ⋊ C4×C11
HallC3×C5×C11×C13 ⋊ C4
HallC5×C11×C13 ⋊ Dic3
HallC3×C11×C13 ⋊ Dic5
HallC3×C5×C11 ⋊ Dic13
HallC11×C13 ⋊ Dic15
HallC5×C13 ⋊ C11×Dic3
HallC5×C11 ⋊ Dic39
HallC3×C13 ⋊ C11×Dic5
HallC3×C11 ⋊ Dic65
HallC3×C5 ⋊ C11×Dic13
SylowC13 ⋊ C11×Dic15
SylowC5 ⋊ C11×Dic39
SylowC3 ⋊ C11×Dic65

Subgroups

subgroupG/H
center, hypercenterC2×C11D195
commutator, hypocenterC3×C5×C13C4×C11
FrattiniC2C11×D195
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×Dic585, C11×C3⋊(Dic65⋊C3), C11×C3⋊Dic195, …
maximal normal subgroup ofC11×C3⋊(Dic65⋊C3), C3×C11×Dic195
maximal quotient ofC11×Dic585, C11×C3⋊Dic195, C3×C11×Dic195

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 17);