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C5⋊D5×C79⋊C3 #26045003

order11850
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

direct productC5⋊D5×C79⋊C3
unambiguous semidirect productC5⋊(D5×C79⋊C3)

Splittings

Fitting, socle, derived, HallC52×C79 ⋊ C2×C3
HallC52×C79⋊C3 ⋊ C2
HallC5⋊D5×C79 ⋊ C3
SylowC79 ⋊ C3×C5⋊D5
SylowC52 ⋊ C2×C79⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C79C2×C3
LCSG ▷ C52×C79
UCSC1

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

406 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C5⋊(D79⋊C3))⋊D5, D52×C79⋊C3, C5⋊D5×D79⋊C3, …
maximal normal subgroup of(C5⋊(D79⋊C3))⋊D5, D52×C79⋊C3, C5⋊D5×D79⋊C3, …
maximal quotient of#1039×C79⋊C3, C2×C5⋊D5×C79⋊C3, C5⋊D5×C79⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11850, 18);