Finite Group Databasebeta

← Prev (#13063400) Next (#13063402) →

C5×Dic3×C23 #13063401

order1380
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic3×C23
unambiguous semidirect productC3⋊(C4×C5×C23)

Splittings

derived, SylowC3 ⋊ C4×C5×C23
HallC3×C5×C23 ⋊ C4
HallC3×C23 ⋊ C4×C5
HallC3×C5 ⋊ C4×C23

Subgroups

subgroupG/H
center, hypercenterC2×C5×C23D3
commutator, hypocenterC3C4×C5×C23
FrattiniC2C5×D3×C23
Fitting, socle, prime radicalC2×C3×C5×C23C2
cosocleC2×C3C2×C5×C23
LCSG ▷ C3
UCSC1 ◁ C2×C5×C23

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 1380

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2,3,4,5)(6,7)(8,9)(10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(6,8,7,9)(11,12)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C23×Dic9, C3×C5×Dic3×C23, C5×C23×C3⋊Dic3, …
maximal normal subgroup ofC3×C5×Dic3×C23, C5×C11×Dic3×C23, C5×Dic3×C23⋊C11, …
maximal quotient ofC5×C23×Dic9, C3×C5×Dic3×C23, C5×C23×C3⋊Dic3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1380, 4);