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(C7⋊D7)⋊D37 #20299797

order7252
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C7⋊D7)⋊D37
unambiguous semidirect productD259⋊D7

Splittings

Fitting, socle, derived, HallC72×C37 ⋊ C22
SylowC72 ⋊ C2×D37
SylowC37 ⋊ D72

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC72×C37C22
LCSG ▷ C72×C37
UCSC1

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,7^2,37|c^a=c^6,e^a=e^36,c^b=c^6,d^b=d^6

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#36344303, #13095537⋊D7, #13095538⋊D7, …
maximal normal subgroup of#13095537⋊D7, #13095538⋊D7, (ΓL(1,𝔽8)⋊D7)⋊D37, …
maximal quotient ofC3×(C7⋊D7)⋊D37, D259⋊D21, #36344487, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7252, 26);