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Cayley diagram

C22⋊D35 #63323

order280
isoclinismisoclinic class of Dic70
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productC22⋊D35

Splittings

FittingC22×C5×C7 ⋊ C2
HallC5×C7 ⋊ D4
SylowC7 ⋊ C22⋊D5
SylowC5 ⋊ C22⋊D7

Subgroups

subgroupG/H
center, FrattiniC2C2×D35
commutator, socle, cosocleC2×C5×C7C22
FittingC22×C5×C7C2
hypercenterC22D35
hypocenterC5×C7D4
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2 ◁ C22

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 140

A minimal faithful permutation representation — 2 generators on 16 points:

(1,2,4,6,7,5,3)(8,9,11,12,10)(14,16);(2,3)(4,5)(6,7)(9,10)(11,12)(13,14)(15,16)

Polycyclic presentation:

2^3,5,7|b^a=bc,d^a=d^4,e^a=e^6

Conjugacy classes & character table

73 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10587952, #10587955, D7×C22⋊D5, …
maximal normal subgroup of#10587952, #10587955, D7×C22⋊D5, …
maximal quotient of#10587900, #10587902, #10587903, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(280, 28);