Finite Group Databasebeta

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Cayley diagram

C2×#6669 #91544

order480
isoclinismisoclinic class of #1201
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#6669

Splittings

HallC3×C5 ⋊ C2×C4⋊C4
SylowC5 ⋊ C2×Dic3⋊C4
SylowC3 ⋊ C2×#683

Subgroups

subgroupG/H
center, hypercenterC23D3×D5
commutatorC2×C3×C5C22×C4
FrattiniC22C2×D3×D5
Fitting, socle, prime radicalC23×C3×C5C22
cosocleC22×C3×C5C23
hypocenterC3×C5C2×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23

184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 18 points:

(1,2)(4,5)(6,7)(8,9)(10,12,13,11)(14,15,17,18,16);(3,4,5)(7,9)(10,11,13,12)(15,16)(17,18);(1,2)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746569, #11748568, #11748572, …
maximal normal subgroup of#11746569, #11748568, #11748572, …
maximal quotient ofC2×#90983, #11748435, #11748436, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 620);