Finite Group Databasebeta

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C3×C23×Dic95 #39910718

order26220
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23×Dic95

Splittings

derived, HallC5×C19 ⋊ C3×C4×C23
HallC3×C5×C19×C23 ⋊ C4
HallC5×C19×C23 ⋊ C3×C4
HallC3×C19×C23 ⋊ Dic5
HallC19×C23 ⋊ C3×Dic5
HallC3×C5×C23 ⋊ Dic19
HallC3×C5×C19 ⋊ C4×C23
HallC5×C23 ⋊ C3×Dic19
HallC3×C19 ⋊ Dic5×C23
SylowC19 ⋊ C3×Dic5×C23
HallC3×C5 ⋊ C23×Dic19
SylowC5 ⋊ C3×C23×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23D95
commutator, hypocenterC5×C19C3×C4×C23
FrattiniC2C3×C23×D95
Fitting, socle, prime radicalC2×C3×C5×C19×C23C2
cosocleC2×C5×C19C2×C3×C23
LCSG ▷ C5×C19
UCSC1 ◁ C2×C3×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26220

Conjugacy classes & character table

6762 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 8);