Finite Group Databasebeta

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C5×C23⋊#64424 #46798933

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23⋊#64424
unambiguous semidirect productC23⋊(C5×#64424)

Splittings

Fitting, socle, HallC5×C72×C23 ⋊ C2×C3
derived, HallC72×C23 ⋊ C2×C3×C5
HallC5×C23×#3861 ⋊ C2
HallC5×C7⋊D161 ⋊ C3
HallC23×#3861 ⋊ C2×C5
HallC7⋊D161 ⋊ C3×C5
HallC5×#3861 ⋊ D23
HallC5×C72 ⋊ C3×D23
Hall#3861 ⋊ C5×D23
HallC5×C23 ⋊ #64424
SylowC72 ⋊ C3×C5×D23
SylowC23 ⋊ C5×#64424

Subgroups

subgroupG/H
center, hypercenterC5C23⋊#64424
commutator, cosocle, hypocenterC72×C23C2×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C23C2×C3
LCSG ▷ C72×C23
UCSC1 ◁ C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 5635

A minimal faithful permutation representation — 3 generators on 42 points:

(1,2,3,4,5)(7,10,11,8,9,12)(14,17,18,15,16,19)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42);(13,14,16,19,18,17,15)(20,21,23,25,27,29,31,33,35,37,39,41,42,40,38,36,34,32,30,28,26,24,22);(6,7,9,12,11,10,8)

Conjugacy classes & character table

1115 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 37);