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C17×#611 #11927451

order1224
isoclinismisoclinic class of Dic18
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×#611

Splittings

FittingC22×C9×C17 ⋊ C2
HallC9×C17 ⋊ D4
SylowC9 ⋊ D4×C17

Subgroups

subgroupG/H
centerC2×C17C2×D9
commutator, cosocleC2×C9C22×C17
FrattiniC2×C3C2×D3×C17
FittingC22×C9×C17C2
socleC2×C3×C17C2×D3
hypercenterC22×C17D9
hypocenterC9D4×C17
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C17 ◁ C22×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 612

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,23,25,24,19,21,20,26,22)(28,30);(19,21)(20,24)(22,23)(25,26)(27,28)(29,30)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1224, 24);