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C5⋊D5×D119 #26045447

order11900
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C5

Aliases

direct productC5⋊D5×D119

Splittings

Fitting, socle, derived, HallC52×C7×C17 ⋊ C22
HallC52×C17 ⋊ C2×D7
HallC52×C7 ⋊ C2×D17
HallC7×C17 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×D119
SylowC17 ⋊ D7×C5⋊D5
SylowC7 ⋊ D17×C5⋊D5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7×C17C22
LCSG ▷ C52×C7×C17
UCSC1

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

854 conjugacy classes — view the full character table.

Relationships

maximal subgroup of((C5⋊D5)⋊ΓL(1,𝔽8))⋊D17, (C5⋊D5)⋊C3×D119, C5⋊D5×C17⋊AGL(1,𝔽7), …
maximal normal subgroup of((C5⋊D5)⋊ΓL(1,𝔽8))⋊D17, (C5⋊D5)⋊C3×D119, C5⋊D5×C17⋊AGL(1,𝔽7), …
maximal quotient ofC3×C5⋊D5×D119, C3⋊(C5⋊D5)×D119, C5⋊D5×D357, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 96);