Finite Group Databasebeta

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C23×Dic109⋊C3 #44473785

order30084
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×Dic109⋊C3
unambiguous semidirect productDic109⋊(C3×C23)
unambiguous semidirect product(C23×Dic109)⋊C3

Splittings

derived, SylowC109 ⋊ C3×C4×C23
HallC23×Dic109 ⋊ C3
HallC23×C109⋊C3 ⋊ C4
HallC23×C109 ⋊ C3×C4
HallDic109 ⋊ C3×C23
HallC109⋊C3 ⋊ C4×C23

Subgroups

subgroupG/H
center, hypercenterC2×C23D109⋊C3
commutator, hypocenterC109C3×C4×C23
FrattiniC2C23×D109⋊C3
Fitting, socleC2×C23×C109C2×C3
prime radicalC2×C23×C109⋊C3C2
cosocleC2×C109C2×C3×C23
LCSG ▷ C109
UCSC1 ◁ C2×C23

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10028

Conjugacy classes & character table

1104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30084, 10);