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C11⋊C5×D93 #23779456

order10230
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D93
unambiguous semidirect productC3⋊(C11⋊C5×D31)

Splittings

Fitting, socle, derived, HallC3×C11×C31 ⋊ C2×C5
HallC3×C31×C11⋊C5 ⋊ C2
HallC11×D93 ⋊ C5
HallC31×C11⋊C5 ⋊ D3
HallC11×C31 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ D31
HallC3×C31 ⋊ C2×C11⋊C5
HallC3×C11 ⋊ C5×D31
SylowC31 ⋊ D3×C11⋊C5
SylowC11 ⋊ C5×D93
SylowC3 ⋊ C11⋊C5×D31

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C31C2×C5
LCSG ▷ C3×C11×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

336 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D93, (C3⋊AGL(1,𝔽11))⋊D31, D3×C11⋊C5×D31, …
maximal normal subgroup ofAGL(1,𝔽11)×D93, (C3⋊AGL(1,𝔽11))⋊D31, D3×C11⋊C5×D31, …
maximal quotient ofC11⋊C5×Dic93, C2×C11⋊C5×D93, C11⋊C5×D279, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 55);