Finite Group Databasebeta

← Prev (#24925310) Next (#24925312) →

C2×#11762245⋊C5 #24925311

order10830
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×#11762245⋊C5
unambiguous semidirect product(C2×#11762245)⋊C5
unambiguous semidirect product(C2×C192⋊C5)⋊C3

Splittings

Fitting, socle, HallC2×C192 ⋊ C3×C5
derived, SylowC192 ⋊ C2×C3×C5
HallC2×C192⋊C5 ⋊ C3
HallC2×#11762245 ⋊ C5
HallC192⋊C5 ⋊ C2×C3
Hall#11762245 ⋊ C2×C5

Subgroups

subgroupG/H
center, hypercenterC2#11762245⋊C5
commutator, cosocle, hypocenterC192C2×C3×C5
FrattiniC1G
Fitting, socleC2×C192C3×C5
LCSG ▷ C192
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#20297971⋊C3, #16864558⋊C5, C4×#11762245⋊C5, …
maximal normal subgroup of#20297971⋊C3, #16864558⋊C5, C4×#11762245⋊C5, …
maximal quotient ofC4×#11762245⋊C5, C22×#11762245⋊C5, C2×#15692429⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10830, 16);