Finite Group Databasebeta

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C2×C52×D77 #21440460

order7700
isoclinismisoclinic class of D77
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×D77
unambiguous semidirect product(C2×C7)⋊(C52×D11)

Splittings

Fitting, socleC2×C52×C7×C11 ⋊ C2
derived, HallC7×C11 ⋊ C22×C52
HallC52×C7×C11 ⋊ C22
HallC52×C11 ⋊ C2×D7
HallC52×C7 ⋊ C2×D11
SylowC11 ⋊ C2×C52×D7
SylowC7 ⋊ C2×C52×D11

Subgroups

subgroupG/H
center, hypercenterC2×C52D77
commutator, hypocenterC7×C11C22×C52
FrattiniC1G
Fitting, socleC2×C52×C7×C11C2
LCSG ▷ C7×C11
UCSC1 ◁ C2×C52

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11⋊(D7⋊(C52⋊C3)), C2×C52⋊C3×D77, C2×C52×C11⋊AGL(1,𝔽7), …
maximal normal subgroup ofC2×C11⋊(D7⋊(C52⋊C3)), C2×C52⋊C3×D77, C2×C52×C11⋊AGL(1,𝔽7), …
maximal quotient ofC52×D3×D77, C2×C3×C52×D77, C2×C52×D231

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 124);