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C2×D7×C11⋊C25 #21440352

order7700
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×D7×C11⋊C25
unambiguous semidirect productC7⋊(C22×C11⋊C25)
unambiguous semidirect product(C2×C7)⋊(C2×C11⋊C25)
unambiguous semidirect product(C2×C11×D7)⋊C25

Splittings

derived, HallC7×C11 ⋊ C22×C25
HallC7×C11⋊C25 ⋊ C22
HallC2×C11×D7 ⋊ C25
SylowC11 ⋊ C2×D7×C25
SylowC7 ⋊ C22×C11⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5D7×C11⋊C5
commutator, hypocenterC7×C11C22×C25
FrattiniC5C2×D7×C11⋊C5
Fitting, socleC2×C5×C7×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

350 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽7)×C11⋊C25, D3×D7×C11⋊C25, C2×C3×D7×C11⋊C25, …
maximal normal subgroup ofC2×AGL(1,𝔽7)×C11⋊C25, C2×C3×D7×C11⋊C25
maximal quotient ofD3×D7×C11⋊C25, C2×C3×D7×C11⋊C25, C2×D21×C11⋊C25

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 16);