Finite Group Databasebeta

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C23⋊((C19⋊C3)⋊Dic5) #39910734

order26220
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC23⋊((C19⋊C3)⋊Dic5)
unambiguous semidirect product(C19⋊C3)⋊Dic115
unambiguous semidirect productDic2185⋊C3

Splittings

derived, HallC5×C19×C23 ⋊ C3×C4
HallDic2185 ⋊ C3
HallC5×C23×C19⋊C3 ⋊ C4
HallC23×C19⋊C3 ⋊ Dic5
HallC19×C23 ⋊ C3×Dic5
HallC5×C19⋊C3 ⋊ Dic23
HallC5×C23 ⋊ (C19⋊C3)⋊C4
HallC5×C19 ⋊ C3×Dic23
HallC19⋊C3 ⋊ Dic115
SylowC23 ⋊ (C19⋊C3)⋊Dic5
SylowC19 ⋊ C3×Dic115
SylowC5 ⋊ C23⋊((C19⋊C3)⋊C4)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C5⋊(C23⋊(D19⋊C3))
commutator, hypocenterC5×C19×C23C3×C4
Fitting, socle, cosocleC2×C5×C19×C23C2×C3
prime radicalC2×C5×C23×C19⋊C3C2
LCSG ▷ C5×C19×C23
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8740

Polycyclic presentation:

2,3,5,19,23,2|a^2=f,c^a=c^4,d^a=d^18,e^a=e^22,d^b=d^7

Conjugacy classes & character table

1044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 24);