Finite Group Databasebeta

← Prev (#63452) Next (#63454) →

Cayley diagram

C4⋊C4×D9 #63453

order288
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×D9

Splittings

FittingC9×C4⋊C4 ⋊ C2
SylowC9 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC22C22×D9
commutatorC2×C9C22×C4
Frattini, socleC22×C3C22×D3
FittingC9×C4⋊C4C2
prime radicalC22×D9C22
cosocleC22×C9C23
hypercenterC4⋊C4D9
hypocenterC9C2×C4⋊C4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4⋊C4

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 144

A minimal faithful permutation representation — 3 generators on 17 points:

(2,4)(3,7)(5,8)(6,9);(1,8,9,3,2,4,7,6,5)(14,15,16,17);(10,11,12,13)(15,17)

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×#102, #10588451, #10588454, …
maximal normal subgroup ofD9×#102, #10588451, #10588454, …
maximal quotient of#10588327, #10588329, #10588330, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 101);