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D4×#11929434 #23757339

order10048
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD4×#11929434

Splittings

SylowC157 ⋊ C8×D4

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D157
commutatorC2×C157C22×C8
FittingC4×D4×C157C2
socleC22×C157C22×C4
prime radicalC2×D4×C157C4
cosocleC2×C4×C157C23
hypercenterC4×D4D157
hypocenterC157C8×D4
LCSG ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C4×D4

134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34098928, D8×#11929434, SD16×#11929434, …
maximal normal subgroup of#34098928, D8×#11929434, SD16×#11929434, …
maximal quotient ofD8×#11929434, SD16×#11929434, Q16×#11929434, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 615);