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D5×C5⋊(C7⋊D7) #19096697

order4900
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C7

Aliases

direct productD5×C5⋊(C7⋊D7)
unambiguous semidirect product(C5×D5)⋊(C7⋊D7)
unambiguous semidirect product(C7×D5)⋊D35

Splittings

Fitting, socle, derived, HallC52×C72 ⋊ C22
SylowC72 ⋊ D52
SylowC52 ⋊ C2×C7⋊D7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC52×C72C22
LCSG ▷ C52×C72
UCSC1

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

496 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C5⋊#64424, D5×C5⋊#64425, D5×C5⋊(ΓL(1,𝔽8)⋊D7), …
maximal normal subgroup ofD5×C5⋊#64424, D5×C5⋊#64425, D5×C5⋊(ΓL(1,𝔽8)⋊D7), …
maximal quotient ofC3×D5×C5⋊(C7⋊D7), D5×C3⋊(C5⋊(C7⋊D7)), D15×C5⋊(C7⋊D7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4900, 101);