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C5×C23×Dic77 #47978375

order35420
automorphism?
homologyAbelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×Dic77
unambiguous semidirect productC7⋊(C5×C23×Dic11)

Splittings

derived, HallC7×C11 ⋊ C4×C5×C23
HallC5×C7×C11×C23 ⋊ C4
HallC7×C11×C23 ⋊ C4×C5
HallC5×C11×C23 ⋊ Dic7
HallC5×C7×C23 ⋊ Dic11
HallC5×C7×C11 ⋊ C4×C23
HallC11×C23 ⋊ C5×Dic7
HallC7×C23 ⋊ C5×Dic11
HallC5×C11 ⋊ C23×Dic7
HallC5×C7 ⋊ C23×Dic11
SylowC11 ⋊ C5×C23×Dic7
SylowC7 ⋊ C5×C23×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C23D77
commutator, hypocenterC7×C11C4×C5×C23
FrattiniC2C5×C23×D77
Fitting, socle, prime radicalC2×C5×C7×C11×C23C2
cosocleC2×C7×C11C2×C5×C23
LCSG ▷ C7×C11
UCSC1 ◁ C2×C5×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35420

Conjugacy classes & character table

9200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 9);