Finite Group Databasebeta

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C3×C23×Dic133 #49144702

order36708
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23×Dic133

Splittings

derived, HallC7×C19 ⋊ C3×C4×C23
HallC3×C7×C19×C23 ⋊ C4
HallC7×C19×C23 ⋊ C3×C4
HallC3×C19×C23 ⋊ Dic7
HallC3×C7×C23 ⋊ Dic19
HallC19×C23 ⋊ C3×Dic7
HallC3×C7×C19 ⋊ C4×C23
HallC7×C23 ⋊ C3×Dic19
HallC3×C19 ⋊ C23×Dic7
HallC3×C7 ⋊ C23×Dic19
SylowC19 ⋊ C3×C23×Dic7
SylowC7 ⋊ C3×C23×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23D133
commutator, hypocenterC7×C19C3×C4×C23
FrattiniC2C3×C23×D133
Fitting, socle, prime radicalC2×C3×C7×C19×C23C2
cosocleC2×C7×C19C2×C3×C23
LCSG ▷ C7×C19
UCSC1 ◁ C2×C3×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36708

Conjugacy classes & character table

9384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36708, 11);