Finite Group Databasebeta

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#117×Dic61 #21448162

order7808
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×Dic61

Splittings

SylowC61 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D61
commutatorC2×C61C22×C42
FrattiniC23C23×D61
FittingC2×#117×C61C2
socleC23×C61C24
hypercenterC2×#117D61
hypocenterC61C4×#117
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#117

752 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1280 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#29573454, #29573458, H(3,ℤ/4)×Dic61, …
maximal normal subgroup of#29573454, #29573458, H(3,ℤ/4)×Dic61, …
maximal quotient of#376×Dic61, C4×C22⋊C4×Dic61, C4×C4⋊C4×Dic61, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7808, 6853);