Finite Group Databasebeta

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C5×C11×Dic145 #44542027

order31900
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic145

Splittings

derivedC5×C29 ⋊ C4×C5×C11
HallC52×C11×C29 ⋊ C4
HallC52×C29 ⋊ C4×C11
HallC11×C29 ⋊ C5×Dic5
HallC52×C11 ⋊ Dic29
SylowC29 ⋊ C5×C11×Dic5
SylowC52 ⋊ C11×Dic29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D145
commutator, hypocenterC5×C29C4×C5×C11
FrattiniC2C5×C11×D145
Fitting, socle, prime radicalC2×C52×C11×C29C2
cosocleC2×C5×C29C2×C5×C11
LCSG ▷ C5×C29
UCSC1 ◁ C2×C5×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6380

Conjugacy classes & character table

8140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31900, 62);