Finite Group Databasebeta

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C11×Dic805 #47978382

order35420
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic805
unambiguous semidirect productC7⋊(C11×Dic115)

Splittings

derived, HallC5×C7×C23 ⋊ C4×C11
HallC5×C7×C11×C23 ⋊ C4
HallC7×C11×C23 ⋊ Dic5
HallC5×C11×C23 ⋊ Dic7
HallC5×C7×C11 ⋊ Dic23
HallC11×C23 ⋊ Dic35
HallC7×C23 ⋊ C11×Dic5
HallC5×C23 ⋊ C11×Dic7
HallC7×C11 ⋊ Dic115
HallC5×C11 ⋊ Dic161
HallC5×C7 ⋊ C11×Dic23
SylowC23 ⋊ C11×Dic35
SylowC7 ⋊ C11×Dic115
SylowC5 ⋊ C11×Dic161

Subgroups

subgroupG/H
center, hypercenterC2×C11D805
commutator, hypocenterC5×C7×C23C4×C11
FrattiniC2C11×D805
Fitting, socle, prime radicalC2×C5×C7×C11×C23C2
cosocleC2×C5×C7×C23C2×C11
LCSG ▷ C5×C7×C23
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35420

Conjugacy classes & character table

8888 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 16);