Finite Group Databasebeta

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C4×C11×#89204 #34084642

order19404
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11×#89204

Splittings

derived, SylowC72 ⋊ C4×C9×C11
HallC4×C72×C11 ⋊ C9
HallC72×C11 ⋊ C4×C9
HallC4×C72 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C4×C11#3861
commutator, hypocenterC72C4×C9×C11
FrattiniC2×C3C2×C11×#3861
FittingC3×C4×C72×C11C3
socle, prime radicalC2×C3×C72×C11C2×C3
cosocleC2×C3×C72C2×C3×C11
LCSG ▷ C72
UCSC1 ◁ C3×C4×C11

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19404

Conjugacy classes & character table

2508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 133);