Finite Group Databasebeta

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C2×C72×D41 #22548824

order8036
isoclinismisoclinic class of D41
automorphism?
homologyAbelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C72×D41
unambiguous semidirect productC41⋊(C22×C72)
unambiguous semidirect product(C2×C41)⋊(C2×C72)

Splittings

Fitting, socleC2×C72×C41 ⋊ C2
derived, SylowC41 ⋊ C22×C72
HallC72×C41 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C72D41
commutator, hypocenterC41C22×C72
FrattiniC1G
Fitting, socleC2×C72×C41C2
LCSG ▷ C41
UCSC1 ◁ C2×C72

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2156 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×ΓL(1,𝔽8)×D41, C2×D41×#3861, C2×D41×#3862, …
maximal normal subgroup ofC2×C7×ΓL(1,𝔽8)×D41, C2×D41×#3861, C2×D41×#3862, …
maximal quotient ofD3×C72×D41, C2×C3×C72×D41, C2×C72×D123

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8036, 34);